I've played the DS and, now, the PSP. I have to say, I prefer the PSP, but it's not for everyone.
The PSP has a lot to offer. It has more "hardcore" games, including a wide array of downloadable games. The controls are difficult to get used to, with the analog stick and direction pad by the same hand. It's tough to get used the the controlling Snake in Metal Gear Solid: Peacewalker, but once you do it's a surprising deep game for a portable system. There's the usual action/stealth gameplay of the Metal Gear series, plus you recruit your team, build your base, research your weapons... basically, there's a lot more to do.
But the main reason I'm writing this review is to warn people as Christmas approaches. This is not a system for little kids. If you have an older gamer (teenager or above) looking for a portable system, I'd recommend the PSP. If you're buying a present for you 8 year old, get them something simpler.